What is the integral from-infinity to 0 of (xe^{2x}) ?

The integral from-infinity to 0 of (xe^{2x}) is -1/4

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integral from-infinity to 0 of (xe^{2x})

\int_{- \infty}^{0} (x e^{2 x}) d x

- \frac{1}{4}

Decimal Notation

- 0.25

Solution steps

\int_{- \infty}^{0} x e^{2 x} d x

Compute the indefinite integral:

\int x e^{2 x} d x = \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} (x e^{2 x}) d x = - \frac{1}{4} - 0

= - \frac{1}{4} - 0

Simplify

= - \frac{1}{4}

\frac{d}{d x} (cos^{4} (3 x^{2}))

n = 1 \sum \infty \frac{1}{n ^{2} + n ^{3}}

x \to 9 lim (7 x - 8)

\frac{\partial}{\partial x} (- 2 ∣ x ∣)

y^{^{''}} - 3 y^{^{'}} + 2 y = x^{2}

What is the integral from-infinity to 0 of (xe^{2x}) ?
The integral from-infinity to 0 of (xe^{2x}) is -1/4